In this section, we discuss several first-order proximal algorithms and
their connections.
We start with four three-operator splitting algorithms
for problem (REF ):
the primal and dual variants of the
Condat–Vũ algorithm [1]}, [2]},
the primal–dual three-operator (PD3O) algorithm [3]},
and the primal–dual Davis–Yin (PDDY) algorithm [4]}.
For each of the four algorithms, we make connections
with other first-order proximal algorithms,
using reduction (i.e., setting some parts in (REF ) to zero)
and the “completion” reformulation (based on extending \(A\)  to
a matrix with orthogonal rows and equal row norms) [5]}.
We focus on the formal connections between algorithms.
The connections do not necessarily provide the best approach
for convergence analysis or the best known convergence results.
